Yes, you are correct. To be "into" something suggests that you feel that you are a part of something. You're engaged with it. You are involved in it. When you start doing something new, at first you feel "outside" of it, and then you "get into it" and it starts to feel natural. You feel like you're a part of it.

A bit of both :-) It means that you have just discovered how it works and you are beginning to enjoy it.